When the brakes are applied on a vehicle traveling on a surface at a given velocity, braking torques are generated at each of the braked wheels. The braking torque causes a retarding or braking force to be generated at the interface between the tire and the surface. The braking forces generated at the wheels then cause a decrease in the vehicle velocity.
Ideally, the braking forces at the wheels increase proportionately as the driver increases the force on the brake pedal. Unfortunately, this is not always the case in braking procedures. As the braking torque and hence the braking force at the wheel is increased, the rotational speed of the braked wheels becomes less than the speed of the vehicle. When the rotational speed of a wheel is less than the vehicle speed, "slippage" is said to occur between the tire and the surface. With further increase in brake torque, the slippage between the tire and the surface increases until lock-up and skidding of the wheel occurs. In most cases, lock-up causes an increase in stopping distance. Lock-up also causes a degradation in directional control due to a reduction in the lateral forces at the wheels.
Both of these problems associated with lock-up were addressed with the advent of anti-lock brake systems (ABS). A basic anti-lock brake system monitors the velocity at each of the wheels, decides whether the wheel is excessively slipping based on these velocity measurements, and modulates the braking pressure accordingly to avoid lock-up. The ABS aids in retaining vehicle stability and steerability while providing shorter stopping distances.
One method by which the state of excessive slipping is identified in the ABS is comparing the velocity of each wheel to a reference speed. The reference speed is an estimate of the true vehicle speed based on current and previous values of the individual wheel velocities. If the velocity of a wheel is significantly less than the reference speed, then the wheel is deemed by the ABS to be excessively slipping. The ABS then reduces the pressure actuating the brake in order to reduce brake torque. The reduction of brake torque allows the friction force at the surface to accelerate the wheel, thereby causing a reduction of the slip in the wheel. Similarly, other criteria can be considered in determining the presence of excessive slip.
After a period of constant braking pressure following the pressure reduction, the pressure actuating the brake is increased until excessive wheel slip occurs again. The cycle of decreasing the brake pressure, maintaining constant brake pressure, and then increasing brake pressure is repeated until the antilock event ends. The parameters which define the specifics of this cycle depend on both the vehicle and the surface conditions.
For the present invention, the braking of a vehicle on a surface with varying coefficient of friction is considered. The coefficient of friction, mu, of a surface is defined as the ratio of the braking force generated at the interface between the tire and the surface, to the normal force between the tire and the surface.
Three classes of surfaces can be defined qualitatively in terms of mu: high-mu, low-mu, and split-mu. A high-mu surface is one which produces relatively good braking ability. Dry asphalt is an example of a high-mu surface. A low-mu surface is characterized by its resulting in poor braking ability. An example of a low-mu surface is a road covered with snow or ice. A split-mu surface is encountered when a vehicle has one or more tires on a latitudinal axis on a low-mu surface and the other tire or tires on the same latitudinal axis on a high-mu surface. An example of a split-mu surface is a road with snow or ice on one side of the vehicle and dry asphalt on the other side of the vehicle.
In relative terms, the coefficient of friction, mu, can also be expressed as a variation from a current or reference mu. Specifically, a higher-mu surface is a surface whose mu is greater than the reference and a lower-mu surface is a surface whose mu is less than the reference.
An example of braking on a split-mu to higher-mu transition can be envisaged based on the previous examples. Consider a vehicle braking on a surface where the left tires are exposed to a cleared section of the road (e.g. asphalt) while the right tires are exposed to snow. In split-mu control, the brake on the right wheel is controlled cyclically while the pressure apply rate to the brake of the left wheel is restricted. After a distance of split-mu braking, the right tires also become exposed to the cleared section of the road. As the vehicle makes the transition from the split-mu surface to the higher-mu surface, the brake pressure at the wheel on the previously lower-mu side (here, the right side) begins to increase in order to increase deceleration. However, the increase in brake pressure causes a torque imbalance with the opposite wheel whose pressure is restricted (here, the left wheel).